Quantum chromodynamics predicts the existence of a phase transition from hadronic to quark-gluon matter when temperature and pressure are sufficiently high. Colliding heavy nuclei at ultra-relativistic speeds allows to d

Quantum chromodynamics predicts the existence of a phase transition from hadronic to quark-gluon matter when temperature and pressure are sufficiently high. Colliding heavy nuclei at ultra-relativistic speeds allows to deposit large amounts of energy in a small volume of space, and is the only available experimental mean to produce the extreme conditions necessary to obtain the deconfined state. Numerous models and ideas were developed in the last decades to study heavy ion physics and understand the properties of extremely heated and compressed nuclear matter. With the ever increasing energy available in the center of mass frame (and thus number of particles produced) and the development of large acceptance detectors, it has become possible to study the fluctuations of physical quantities on an event-by-event basis, and access thermodynamical properties not present in particle spectra. The characteristics of the highly excited matter produced, e.g. thermalization, effect of resonance decay. . . can be investigated by fluctuation analyses. In fact, fluctuations are good indicators for a phase transition and a plethora of fluctuation probes have been proposed to pin down the existence and the properties of the QGP. We study various fluctuation quantities within the Ultra-relativistic Quantum Molecular Dynamics UrQMD and the quantum Molecular Dynamics qMD models. UrQMD is based on hadron and string degrees of freedom and allows to disentangle purely hadronic effects. In contrast, the qMD model includes an explicit transition from quark to hadronic matter and can serve to test adequate probes of the initial QGP state. We show that the qMD model can reasonably reproduce various experimental particles rapidity distributions and transverse mass spectra in wide energy range. Within the frame of the dynamical recombination procedure used in qMD, we study the enhancement of protons over pions (p/&#960;) ratio in the intermediate pt range (1.5 < pt < 2.5). We show that qMD can reproduce the large p/&#960; &#8776; 1 observed experimentally at RHIC energies at hadronization. However, the subsequent decay of resonances makes the ratio fall to values incompatible with experimental data. We thus conclude that resonance decay might have a drastic influence on this observable in the quark recombination picture. Charged particles multiplicity fluctuations measured at SPS by the NA49 collaboration are enhanced in midperipheral events for Pb+Pb collisions at Elab = 160 AGeV. This feature is not reproduce by hadron-string transport approaches, which show a flat centrality dependence, within the proper experimental acceptance and with the proper centrality selection procedure. However, we show that the behavior of multiplicity fluctuations in transport codes is similar to the experimental result in full 4&#960; acceptance. We identify the centrality selection procedure as the reason for the enhanced particle multiplicity fluctuations in midperipheral reactions and argue that it can be used to distinguish between different scenarios of particle productions. We show that experimental data might indicate a strong mixing of projectile and target related production sources. Strangeness over entropy K/&#960; and baryon number over entropy p/&#960; ratio fluctuations have been measured by the NA49 experiment in the SPS energy range, from Elab = 20 AGeV up to Elab = 160 AGeV. We investigate the sensitivity of this observable to kinematical cuts and discuss the influence of resonance decay. We find the dynamical p/&#960; ratio fluctuations to increase with beam energy, in agreement with the measured data points. On the contrary, the dynamical K/&#960; ratio fluctuations are essential flat as a function of centrality and depend only weakly on the kinematical cuts applied. Our results are in line with the simulations performed earlier by the NA49 collaboration in their detector acceptance filter. Finally, we focus on the correlations and fluctuations of conserved charges. It was proposed that these fluctuations are sensitive to the fractional charge carried by the quarks in the initial QGP stage and survive the whole course of heavy ion reactions. A crucial point is the influence of hadronization that may relax the initial QGP fluctuation/correlation signals to their hadronic values. We use the quark Molecular Dynamics qMD model to disentangle the effect of recombination-hadronization on charged particles ratio fluctuations, charge transfer fluctuations, baryon number-strangeness correlation coefficient and various ratios of susceptibilities (i.e. correlations over fluctuations). We find that the dynamical recombination procedure implemented in the qMD model destroys all studied initial QGP fluctuations and correlations and might ex- plain why no signal of a phase transition based on event-by-event fluctuations was found in the experimental data until now.